In the last hour, ellie observed 32 monarchs, 56 gulf fritillaries and 8 giant swallowtails visit her butterfly garden. 0 i if 480 butterflies visit her garden, how many can we expect will be giant swallowtails?

40

Step-by-step explanation:

Developing an initial ratio of the number of giant swallowtails to the total number of observed butterflies, you can then use this ratio to form a proportion (equivalent ratios) to solve for the amount of giant swallowtails expected out of 480:

Since 32 + 56 + 8 = 96, then the original ratio is 8/96.  To find the expected number out of 480:

, where 'x' is the number of giant swallowtails

Cross-multiply: 96x = (8)(480) or 96x = 3840

Divide: 96x/96 = 3840/96

Solve: x = 40

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15